Remove the absolute value term. This creates a <math><mstyle displaystyle="true"><mo>±</mo></mstyle></math> on the right side of the equation because <math><mstyle displaystyle="true"><mrow><mo>|</mo><mi>x</mi><mo>|</mo></mrow><mo>=</mo><mo>±</mo><mi>x</mi></mstyle></math> .

First, use the positive value of the <math><mstyle displaystyle="true"><mo>±</mo></mstyle></math> to find the first solution.

Move all terms not containing <math><mstyle displaystyle="true"><mi>w</mi></mstyle></math> to the right side of the equation.

Subtract <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> from both sides of the equation.

Subtract <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>39</mn></mstyle></math> .

Divide each term in <math><mstyle displaystyle="true"><mo>-</mo><mn>6</mn><mi>w</mi><mo>=</mo><mn>36</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>6</mn></mstyle></math> and simplify.

Divide each term in <math><mstyle displaystyle="true"><mo>-</mo><mn>6</mn><mi>w</mi><mo>=</mo><mn>36</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>6</mn></mstyle></math> .

Simplify the left side.

Cancel the common factor of <math><mstyle displaystyle="true"><mo>-</mo><mn>6</mn></mstyle></math> .

Cancel the common factor.

Divide <math><mstyle displaystyle="true"><mi>w</mi></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Simplify the right side.

Divide <math><mstyle displaystyle="true"><mn>36</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>6</mn></mstyle></math> .

Next, use the negative value of the <math><mstyle displaystyle="true"><mo>±</mo></mstyle></math> to find the second solution.

Move all terms not containing <math><mstyle displaystyle="true"><mi>w</mi></mstyle></math> to the right side of the equation.

Subtract <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> from both sides of the equation.

Subtract <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> from <math><mstyle displaystyle="true"><mo>-</mo><mn>39</mn></mstyle></math> .

Divide each term in <math><mstyle displaystyle="true"><mo>-</mo><mn>6</mn><mi>w</mi><mo>=</mo><mo>-</mo><mn>42</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>6</mn></mstyle></math> and simplify.

Divide each term in <math><mstyle displaystyle="true"><mo>-</mo><mn>6</mn><mi>w</mi><mo>=</mo><mo>-</mo><mn>42</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>6</mn></mstyle></math> .

Simplify the left side.

Cancel the common factor of <math><mstyle displaystyle="true"><mo>-</mo><mn>6</mn></mstyle></math> .

Cancel the common factor.

Divide <math><mstyle displaystyle="true"><mi>w</mi></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Simplify the right side.

Divide <math><mstyle displaystyle="true"><mo>-</mo><mn>42</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>6</mn></mstyle></math> .

The complete solution is the result of both the positive and negative portions of the solution.

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